Message passing neural network (MPNN) has recently emerged as a successful framework by achieving state-of-the-art performances on many graph-based learning tasks. MPNN has also recently been extended to multi-relational graphs (each edge is labelled), and hypergraphs (each edge can connect any number of vertices). However, in real-world datasets involving text and knowledge, relationships are much more complex in which hyperedges can be multi-relational, recursive, and ordered. Such structures

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... present several unique challenges because it is not clear how to adapt MPNN to variable-sized hyperedges in them. In this work, we first unify exisiting MPNNs on different structures into G-MPNN (Generalised-MPNN) framework. Motivated by real-world datasets, we then propose a novel extension of the framework, MPNN-R (MPNN-Recursive) to handle recursively-structured data. Experimental results demonstrate the effectiveness of proposed instances of G-MPNN and MPNN-R. The code is available. 1